Shockingly, Egyptologists study Egypt. How they study her is open to interpretation, since the field is not technically a science field, but rather part of the humanities. There are as many kinds of Egyptologists as there are (or were) things in Egypt. (Over the centuries, grave robbers stole a bunch of it to list on eBay.) Everything from the Indiana Jones type (the Egyptian archaeologist) scaling pyramids with one hand on the rock and the other firmly clamped to his leather hat, to the Daniel Jackson type (the Egyptian philologist), feverishly working out inscriptions so the U.S. government can fire up a stargate, is included under the banner of Egyptology.
Egyptologists work in academia as translators, historians, art historians, instructors, and researchers. Why? Because the goal here is to… figure out the past. They may work in museums as curators, registrars, researchers, and exhibit creators. While tourism drives the economy of Egypt, that rarely motivates Egyptologists. Few work in actual tourism, even though their work encourages it. Most are academic types, or interested in archaeological fortune and glory. While there's a lot of conversation about what the Arab Spring and changes in Egypt mean to the field, mostly it's couched in terms of "what if they decide we can't dig there anymore?" or "what if they close the museums?" and not really about Egyptians at all, sad to say.
Egyptologists trained in archaeology (also called Egyptian archaeologists) research and conduct excavations in Egypt to add to and further explain our body of knowledge about Egypt, or they survey and record such excavations, so future Egyptologists will have things to write about.
Not the safest place to play hide and seek.
Egyptologists sometimes appear in public lectures or on television, as “talking heads” in documentaries, or consultants to films like The Mummy (yes, a real Egyptologist told them exactly how Imhotep should cuss out his girlfriend at the end). All periods of Egyptian history and culture are included, though most Egyptologists focus on what is called the pharaonic period, from about 4000 BCE and lasting until that time Cleopatra VII fell on her asp in the summer of 30 BCE. (Hint: if you really want a job in Egyptology, there are far more openings in non-pharaonic research, and particularly in the study of Egypt since the Islamic conquest in the 7th Century CE to the present day.)
Becoming an Egyptologist requires many years of education, and, since the field is currently overextended (there is probably 1 job for every 5 trained Egyptologists right now, making it awfully tough for newbies to squeeze their way in when there already aren’t enough jobs for established Egyptologists), careful planning and specialization toward the needs of a particular potential employer or subfield is mandatory.
Unlike medicine, there is no such thing as an Egyptologist in general practice. Every successful Egyptologist has one or more narrow (and often obscure) specialty, guaranteed to create job security and improve his or her odds of standing out to whatever museum, university, or other research institution that (s)he wants to work for.
If you really think you’re going to be hired to study ancient beer jars from that Abydos dig when you spent seven years writing a dissertation on 26th Dynasty leather shoes, think again. If you’re lucky, you’re related to people already in the field, or you’ve spent years impressing prominent scholars, so that when it comes time to divide those two internship positions on the next dig between the 1,200 people who sent in applications, you’re likely to make it past the first round. Each archaeologist hires for his own dig, and because of the surplus of available people, is unlikely they will choose someone who doesn't have the precise specialty they want to do a specialized job. In reality, most digs end up being populated by an archaeologist's family, personal students, financial backers, and friends. It is possible to get an "in" to that old digger's club... if you have the exact skills they require. Other archaeologists can be this insular, but most of those fields are a little more open than Egyptology, since it's specific to one country and controlled by a small number of government-directed or university-directed concessions.
What do people do when they wash out of this gig? Whatever they can, as often as they can. You can continue to study in the hopes of getting picked up elsewhere, fall back on your other background in accounting, audition for The Voice. Whatever pays the bills.
There is a large number of Egyptologists and a dwindling number of Egyptology jobs. This mainly has to do with the economy - universities are cutting programs, museums are not hiring, tourists are not going to Egypt, etc. It's still a little early to tell what effect the Egyptian revolution will have on the field overall. It is definitely throwing a wrench and delays into the concession process, while the provisional government makes up its mind about who is running the Supreme Council of Antiquities, and thus who is working with the foreign concessions. For this reason, and because the field necessitates a high degree of education and specialization, Egyptologists themselves can be territorial creatures.
Choose your specialization carefully. Once chosen, like the Highlander, there can be only one, and Egyptologists in other subfields will likely view you with contempt, or no longer be interested in working with you. It's a very small group of people with little concern for the outside world on the academic side, and on the archaeology side you have non-scholars with lots of money digging holes who want to be on television. The field was happy to remain small and obscure, and then a few feature films and important discoveries made it into the media, flooding the schools with new blood that doesn't quite match the established “monied grandchildren of Victorian discoverers” template. This contrast between foreigners in their ivory towers and native Egyptians entering the field, or the professors versus the discoverers, sets up some really intense (and totally unfortunate) rivalry.
Should you decide to change your specialization in the midst of school, or later in your career, convincing people in a line of work you once snubbed to like you again is akin to trying to win back a girlfriend after she finds out you cheated on her with her best friend. It’s far better to generalize in your undergraduate years, find out what you’re good at, and then choose a specialization. Hell hath no fury like an advisor scorned, and the divide between specialties (and particularly the academic-oriented specialties and more “general public” oriented specialties like museum work or archaeology) is more like the Nile Valley than a dotted line on an organizational chart.
The Nile Valley, and Egypt’s famous “random red arrow.”
Once you’ve navigated the deserts of long education and competition and landed an Egyptology job, you’ll be able to laugh in hindsight, but until then, keep that laughter to yourself. Humanities or not, this field is at least as competitive as medical school. The more prestigious schools accept maybe one student from a thousand applicants, and half the time, that student won’t even make it to the second year. Once their dream has fossilized, they may go to work in a laundry, write books, make photocopies in a university library, join the military, or teach in other disciplines. You will have to be smart, but you’ll also have to be stubborn, and have the requisite obsession to persevere through many necessary and unnecessary obstacles to a paying career in Egyptology. If you simply want to know more about Egypt or maybe “do something” with it, become a docent at a museum with an Egyptology exhibit or join an Egyptological society or internet mailing list about Egypt. If you’re in this for the “fortune and glory, kid,” like Indy described, you’re in for quite an adventure before you’ll get anywhere near that Lost Ark.